I am wondering what the difference is between using the geometric mean and the product formula when calculating investment returns?

Taking 3 monthly returns, adding 1 to each. I then use the geomean formula of that range less 1. Then do the same with the product formula and get a very different answer.

What's the right approach? I always thought geomean was correct for chain-linking investment returns but when I think about it, it's only returning the geometric mean-- ie the average distance around the mean.

When do you use geomean then?

For example, monthly returns are:

0.41%
0.41%
0.42%

geomean gives me 0.41%
product gives me 1.25%